Curriculum Map: 2012-2013 Mathematics State Standards 6th Grade Q1 (8/14/2012-10/12/2012) Ratios and Proportions Understand ratio concepts and use ratio reasoning to solve problems. What is a ratio? How can a ratio be used to compare two quantities? Why is it important to understand how ratios and unit rates are used in the real world? What kinds of situations would make knowledge of ratios and unit rates important to students? Develop an understanding of concepts and terminology related to ratios. Be able to describe relationships between two quantities. Develop understanding of a unit rate and language associated with unit rates a/b where b cannot equal zero. Be able to solve real-world and mathematical problems using rates and ratios by using tables of equivalent ratios; find missing values in tables; us tables to compare ratios. Be able to plot pairs of values in a coordinate plane. Solve unit rate problems involving unit pricing and constant speed. Find a percent of a quantity as a rate per 100; solve problems involving finding the whole when given a part and the percent. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6: 6.RP,, 6.RP.1, 6.RP.2, 6.RP.3, 6.RP.3.a, 6.RP.3.b, 6.RP.3.c, 6.RP.3.d. Modeling. Quizzes Number Sense Apply and extend previous understandings of multiplication and division to divide fractions by fractions. How can you use quotients of fractions to find out how to share portions, or determine width from length and area? How can a visual model of an equation be created to demonstrate the process of division of fractions? Interpret and compute quotients of fractions Solve word problems involving division of fractions by fractions Using visual fraction models and equations to represent a problem NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6: 6.NS,, 6.NS.1
Compute fluently with multi-digit numbers and find common factors and multiples Can the long division standard algorithm be used efficiently? What are the similarities and differences between a factor and a multiple? Where is the decimal point placed when adding, subtracting, multiplying and dividing? How will we use adding, subtracting, multiplying, and dividing whole numbers and decimals in everyday life? How do you find the GCF and LCM? How are prime numbers used to find GCF and LCM? Students will: Fluently divide multi-digit numbers using the standard algorithm Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation Find the greatest common factor of two whole numbers less than or equal to 100 and least common multiple of two whole numbers less than or equal to 12 Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6:, 6.NS.2, 6.NS.3, 6.NS.4 Problem solving activities Word problems using distributive property Real world word problems Online Resources Comprehensive quizzes and tests Number System: Apply and extend previous understandings of numbers to the system of rational numbers What is a rational number? What is the relationship between a positive and negative integer? How are positive and negative numbers used to represent real world situations? What is the meaning of zero in real world situations? Where is the opposite of a number located on a number line? Based on the signs of an ordered pair, in which quadrant would its point appear? How is an ordered pair plotted on a coordinate plane? Why is it important to be able to find positive and negative points on horizontal and vertical number lines, as well as in a coordinate plane? Understand that positive and negative numbers are used together to describe quantities having opposite directions or values Use positive and negative numbers to represent quantities in real-world contexts Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates Recognize opposite of the opposite of a number is the number itself Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes Find and position integers and other rational numbers on a horizontal or vertical number line diagram Find and position pairs of integers and other rational numbers on a coordinate plane. NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6: 6.NS.5, 6.NS.6, 6.NS.6.a, 6.NS.6.b, 6.NS.6.c
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Q2 (10/15/2012-12/21/2012) Apply and extend previous understandings of numbers to the system of rational numbers. What is absolute value? What is magnitude? How are magnitude and absolute value related? How is the number line oriented and labeled? What is an inequality? How is the correct inequality symbol chosen? Explain inequalities used in real-world situations. How do the values of two negative numbers compare? As a negative number decreases, what happens to its absolute value? How can real-world problems be solved using the coordinate system? Understand ordering and absolute value of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Understand the absolute value of a rational number as its distance from 0 on the number line Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. Understand the absolute value of a rational number as its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6: 6.NS.7, 6.NS.7.a, 6.NS.7.b, 6.NS.7.c, 6.NS.7.d, 6.NS.8 Expressions and Equations: Apply and extend previous understandings of arithmetic to algebraic expressions Why is it important to understand the order of operations in solving algebraic expressions and equations? How is an expression evaluated that includes exponents? How are verbal models translated into mathematical expressions? In a given expression, can the mathematical terms be identified? How do properties of operations help prove expressions are equivalent? What does an exponent tell us to do with the base number? Write and evaluate numerical expressions involving whole-number exponents Write, read, and evaluate expressions in which letters stand for numbers Write expressions that record operations with numbers and with letters standing for numbers Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) View one or more parts of an expression as a single entity Evaluate expressions at specific values of their variables Include expressions that arise from formulas used in real-world problems Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6: 6.EE,, 6.EE.1, 6.EE.2, 6.EE.2.a, 6.EE.2.b, 6.EE.2.c, 6.EE.3, 6.EE.4
. Comprehensive Quizzes and Tests Curriculum Mapping Reason about and solve one-variable equations and inequalities. How can substitutions be used to make an equation or inequality true? What are non-negative rational numbers? How can equations be solved with non-negative rational numbers? How can properties of equality help to solve one-step equations? How can inverse operations to used to solve one-step equations? What is a constraint? What is a condition? Understand solving an equations or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all non negative rational numbers Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely manty solutions; represent solutions of such inequalities on number line diagrams NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6:, 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8. Comprehensive Quizzes and Tests Expressions and Equations: Represent and analyze quantitative relationships between dependent and independent variables. What are dependent and independent variables? What is the relationship between a dependent and an independent variable? Use variables to represent two quantities in a real-world problem that change in relationship to one another Write an equation to express one quantity, thought of as the dependent variable, in terms of the quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6: 6.EE.9,
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Q3 (1/7/2013-3/8/2013) Geometry: Solve real-world and mathematical problems involving area, surface area, and volume How can the area of complex figures be found? Is L x W x H the same as the area of the base x height? How can unit cubes be used to find the volume of right rectangular prisms? How can a coordinate plane be used to solve problems in geometry? How can nets be used to find surface area? Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the sae first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6: 6.G.1, 6.G.2, 6.G.3, 6.G.4, 6.G, Statistics and Probability Develop understanding of statistical variability What is a statistical question? How can data be interpreted using center, spread, and overall shape? How does a measure of center for numerical data differ from a measure of variation? Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its value vary with a single number. NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6: 6.SP.1, 6.SP.2, 6.SP.3
Statistics and Probability: Summarize and describe distributions How can data be displayed? What is an observation? How is data accurately collected? What is inter-quartile range? What does it mean to deviate from a pattern? How does an outlier affect the overall pattern in a set of data? How does the shape of the data distribution affect the choice of measure of center? Display numerical data in plots on a number line, including dot plots, histogram, and box plots. Summarize numerical data sets in relation to their context, such as by: Reporting the number of observations Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Giving quantitative measures of center (median and/or mean) and variability (inter quartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Grade 6: 6.SP.4, 6.SP.5, 6.SP.5.a, 6.SP.5.b, 6.SP.5.c, 6.SP.5.d
Q4 (3/11/2013-5/22/2013) Mathematical Practices How do you know your answer is correct? What steps can be used to check your answers? How do you determine what steps to use when working a word problem? Identify which tools to use in problem-solving. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. NGA Center/CCSSO: State Standards: College- and Career-Readiness Standards and K-12 Mathematics: Mathematical Practices: 1.A, 2.A, 3.A, 4.A, 5.A, 6.A, 7.A, 8.A Students assess reasoning of others and write persuasive arguments for or against their problem-solving method. State practice test and state testing.. Quizzes. Check that students are using appropriate vocabulary.